Multiple-input multiple-output (MIMO) is a family of techniques that utilize multiple antennas at the transmitter and/or at the receiver to exploit the spatial dimension in order to improve data throughput and transmission reliability. The data throughput can be increased by either spatial multiplexing or beamforming. Spatial multiplexing allows multiple data streams to be transmitted simultaneously to the same user through parallel channels in the MIMO setting. This is especially true for diversity antennas where spatial correlation is low between antennas (both at the transmitter and the receiver). Beamforming helps to enhance the signal-to-interference-plus-noise ratio (SINR) of the channel, thus improving the channel rate. Such SINR improvement is achieved by proper weighting over multiple transmit antennas and the weight calculation can be based on either long-term measurement (e.g., open-loop) or via feedback (e.g., closed-loop). Closed-loop transmit weighting is often called precoding in the context of MIMO study.
References to background prior art include the following publications:    (1) 3GPP TR 36.814, v1.1.1, “Further Advancements for E-UTRA, Physical Layer Aspects”, June 2009; and    (2) 3GPP TS 36.211, “Evolved Universal Terrestrial Radio Access (E-UTRA); Physical Channels and Modulation”.
A MIMO broadcast channel can be described as follows, where there is K receiver and the transmitter has M>1 antennas:yi=hi·x+ni,i=1,2, . . . K  (0.1),with E[∥x∥2]<P.
When linear precoding is used, the transmitter multiplies the signal intended for each user with a beamforming vector, and transmits the sum of these vector signals:
                                          y            i                    =                                                    ∑                                  j                  =                  1                                K                            ⁢                                                          ⁢                                                h                  i                                ·                                  v                  i                                ·                                  s                  i                                                      +                          n              i                                      ,                            (        0.2        )            where v denotes the beamforming vector.
Beamforming vectors can be based on the zero-forcing principle, in which the beamforming vector for user equipment (UE) is chosen to be orthogonal to the channel vector of all other users.
Linear precoding performance depends on the choice of beamforming vectors, which is decided from the channel feedback from each UE. To achieve the capacity of a multi-user MIMO channel, the accurate channel state information is necessary at the transmitter. However, in real systems, receivers feedback the partial channel state information to the transmitter in order to efficiently use the uplink feedback channel resource, which is the multi-user MIMO system with limited feedback precoding.
When there is an imperfection of this channel knowledge, some degree of multiuser interference is inevitably introduced, leading to performance degradation. An example of such imperfection is quantization. Quantization error is related to the bits used. It can be seen that quantization error ζ can be bounded as follows:
                                                        (                                                M                  -                  1                                M                            )                        ·                          2                              -                                  B                                      M                    -                    1                                                                                <          ϛ          <                      2                          -                              B                                  M                  -                  1                                                                    ,                            (        0.3        )            where M is the total number of transmit antennas and B is the total bits used to quantize the feedback. To further analyze and quantify the performance degradation caused by imperfect feedback, system rate loss can be defined as follows:
                              Δ          ⁢                                          ⁢          δ          ⁢                                          ⁢                      (            P            )                          =                              1            M                    ⁢                                    ∑                              j                =                1                            K                        ⁢                                                  ⁢                                          [                                                      R                    ⁡                                          (                      P                      )                                                        -                                                            R                      _                                        ⁡                                          (                      P                      )                                                                      ]                            .                                                          (        0.4        )            
It can be shown that:
                              Δ          ⁢                                          ⁢                      δ            ⁡                          (              P              )                                      <                  K          ·                                                    log                2                            ⁡                              (                                  1                  +                                      P                    ·                                          2                                              -                                                  B                                                      M                            -                            1                                                                                                                                              )                                      .                                              (        0.5        )            
According to Equation 0.5, rate loss is an increasing function of the system P: signal-to-noise ration (SNR). In other words, in order to maintain a bounded rate loss, the number of feedback bits per mobile needs to be scaled. This can be expressed in another format: If we fix the feedback bits per UE, then the rate that each UE can be achieved by quantized feedback is bounded by
                                          R            FB                    ⁡                      (            P            )                          ≤                  M          ⁡                      (                          1              +                                                B                  +                                                            log                      2                                        ⁢                    e                                                                    M                  -                  1                                            +                                                log                  2                                ⁡                                  (                                      M                    -                    2                                    )                                            +                                                log                  2                                ⁢                e                                      )                                              (        0.6        )            as SNR is approaching infinity.